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2024 Journal Impact Factor - 0.6
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ISSN 2083-6473
ISSN 2083-6481 (electronic version)
Editor-in-Chief
Associate Editor
Prof. Tomasz Neumann
Published by
TransNav, Faculty of Navigation
Gdynia Maritime University
3, John Paul II Avenue
81-345 Gdynia, POLAND
e-mail transnav@umg.edu.pl
Global Stability of Fractional Feedback Systems with Positive Linear Parts
1 Bialystok University of Technology, Białystok, Poland
ABSTRACT: The global (absolute) stability of fractional nonlinear systems with negative feedbacks and positive not necessary asymptotically stable linear parts is addressed. It is shown that the coefficients of the transfer matrix of fractional positive asymptotically stable systems are positive. Sufficient conditions for the global stability of the fractional nonlinear systems with positive linear parts are established.
KEYWORDS: Nonlinear Systems, Fractional Calculus, Stability of systems, Control systems, Positive systems, Lyapunov stability, Transfer functions, State-space models
REFERENCES
Berman A. and Plemmons R.J.: Nonnegative Matrices in the Mathematical Sciences, SIAM, 1994. - doi:10.1137/1.9781611971262
Borawski K.: Modification of the stability and positivity of standard and descriptor linear electrical circuits by state feedbacks, Electrical Review, vol. 93, no. 11, 2017, 176-180. - doi:10.15199/48.2017.11.36
Busłowicz M., Kaczorek T.: Simple conditions for practical stability of positive fractional discrete-time linear systems, Int. J. Appl. Math. Comput. Sci., vol. 19, no. 2, 2009, 263-169. - doi:10.2478/v10006-009-0022-6
Farina L., Rinaldi S.: Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000. - doi:10.1002/9781118033029
Kaczorek T.: Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems, Computational Problems of Electrical Engineering, vol. 5, no. 1, 2015, 11-16. - doi:10.1109/CPEE.2015.7333337
Kaczorek T.: Analysis of positivity and stability of fractional discrete-time nonlinear systems, Bull. Pol. Acad. Sci. Techn., vol. 64, no. 3, 2016, 491-494. - doi:10.1515/bpasts-2016-0054
Kaczorek T.: Global stability of nonlinear feedback systems with positive linear parts, International Journal of Nonlinear Sciences and Numerical Simulation. 2019 (in Press). - doi:10.24425/bpas.2019.127337
Kaczorek T.: Positive 1D and 2D Systems, Springer-Verlag, London, 2002. - doi:10.1007/978-1-4471-0221-2
Kaczorek T.: Positive linear systems with different fractional orders, Bull. Pol. Acad. Sci. Techn., vol. 58, no. 3, 2010, 453-458. - doi:10.2478/v10175-010-0043-1
Kaczorek T.: Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. on Circuits and Systems, vol. 58, no. 7, 2011, 1203-1210. - doi:10.1109/TCSI.2010.2096111
Kaczorek T.: Positive fractional continuous-time linear systems with singular pencils, Bull. Pol. Acad. Sci. Techn., vol. 60, no. 1, 2012, 9-12. - doi:10.2478/v10175-012-0002-0
Kaczorek T.: Descriptor positive nonlinear systems, Advances in Intelligent Systems and Computing, vol. 550, 2017, Springer, 34-44. - doi:10.1007/978-3-319-54042-9_3
Kaczorek T.: Selected Problems of Fractional Systems Theory, Springer, Berlin 2011. - doi:10.1007/978-3-642-20502-6
Kaczorek T.: Stability of fractional positive nonlinear systems, Archives of Control Sciences, vol. 25, no. 4, 2015, 491-496. - doi:10.1515/acsc-2015-0031
Kaczorek T.: Superstabilization of positive linear electrical circuit by state-feedbacks, Bull. Pol. Acad. Sci. Techn., vol. 65, no. 5, 2017, 703-708. - doi:10.1515/bpasts-2017-0075
Kaczorek T.: Theory of Control, vol. 2, PWN, Warsaw, 1981 (in Polish).
Kaczorek T., Borawski K.: Stability of Positive Nonlinear Systems, Proc. MMAR 2017, Międzyzdroje, 28-31.08.2017. - doi:10.1109/MMAR.2017.8046890
Kudrewicz J.: Ustoicivost nieliniejnych sistem z obratnoj swjazju, Avtomatika i Telemechanika, vol. 25, no. 8, 1964.
Lyapunov A.M.: Obscaja zadaca ob ustoicivosti dvizenija, Gostechizdat, Moskwa, 1963.
Leipholz H.: Stability Theory, New York Academic Press, 1970.
Citation note:
Kaczorek T.: Global Stability of Fractional Feedback Systems with Positive Linear Parts. TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 19, No. 1, doi:10.12716/1001.19.01.39, pp. 333-337, 2025
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